Clear double-sided tape. Or clear mounting tape, it's a lot thicker.
...Backing it with aluminum HVAC tape secures the LED from all sides, acts as a reflector housing, and keeps the light from bleeding out under the body. Plus if you scuff up the tape before you put it on you can paint it so it looks better with the body off.
Can also use clear liquid electrical tape.
...Paint it on until you're confident the light will stay put then back it with silver paint followed by black for increased light reflection.